At what point should I sign up for a game

because I dont want to wait 3 weeks to play something but they never reply when the game starts in 2 hours.

I would sign up at least a week in advance, and two seems pretty fair. It probably helps the GM plan by knowing how many players, and it gives them time to talk to you about your character and background and add them to the story.

Most games have dozens of applications because there are significantly more players than GMs. The earlier you can respond the better - if a game is posted for several weeks away, the GM is probably planning on using that time to interview applicants and figure out who to bring into the game. If you are applying a few hours before a game starts, then there is very little chance of getting in - the GM has already chosen players, they may have already all created characters, etc. Getting into a game is often a process because of the imbalance of players to GMs, and don't expect to get into the first game you apply for. If you can't stand waiting for a game, watch for pickup games in the LFG tool, you might have better luck with that.

That is one of those "How long is a piece of string" questions. Unless it is a pick up game, very few GMs are going to let a last minute applicant in. I tend to post games about four to six weeks in advance. Who the players are is critical to a long game, a one shot or a short run, you can wrangle all but the most disruptive players. If you are going to be spending one evening a week for months, possibly years, you are going to be a bit more careful. It all comes down to the GM, but weeks are better than days and days are better than hours.

I sometimes get people asking to join in the hour before a session starts. They don’t get to play that session.